A number of thermoplastic copolyester elastomers have been developed and are available commercially for specific end uses. For example, one such thermoplastic elastomer may contain flame retardants. Another such elastomer may contain segmented copolymer units which impart hardness to the elastomer. Because each copolyester elastomer may contain differing recurring block units, the range of their optimum extrusion temperatures may be very different, and in many instances, will not overlap. Thus, if two such copolyester elastomers are attempted to be melt processed together, such as by extrusion or injection molding, one may be completely melted or damaged from overheating and the other either not melted or only partially melted, resulting in lumps or grains in the resulting material. Yet, because it is often desirable to blend two or more types of thermoplastic polyester elastomers to impart particular properties to the resulting melt processed material, it would be desirable to find a way to melt process such blends to obtain a uniformly melted product.